1. Field of the Invention
The present invention relates to blind selective mapping (BSLM) and blind partial transmit sequence (BPTS) schemes with low decoding complexity for peak to average power ratio (PAPR) reduction of an orthogonal frequency division multiplexing (OFDM) signal. More particularly, the present invention relates to BSLM and BPTS schemes with low decoding complexity for PAPR reduction of an OFDM signal, in which m-sequences are used as phase sequences and a maximum likelihood (ML) decoder with low decoding complexity is used, so that a receiver can decide the phase sequence used in the transmitter, thereby decreasing decoding complexity while minimally degrading bit error rate (BER) performance.
2. Description of the Related Art
Orthogonal frequency division multiplexing (OFDM) is an efficient method for high speed data transmission in multipath fading. In addition, it is possible to significantly enhance the throughput by adapting a data rate per subcarrier from decomposition of a wideband channel. However, a major disadvantage of OFDM is the high peak to average power ratio (PAPR) of the transmitter's output signal, where the range of PAPR is proportional to the number of subcarriers. Due to the high PAPR feature, an OFDM signal can suffer significant inter-modulation and undesired out-of-band radiation when it passes through nonlinear devices, e.g., a high power amplifier (HPA).
Several PAPR reduction schemes have been proposed such as clipping and filtering, coding, selected mapping (SLM), partial transmit sequence (PTS), and tone reservation (TR). SLM and PTS, symbol scrambling techniques, can reduce the peak power of OFDM signals without signal distortion. The key idea of SLM is that the OFDM signal with the smallest PAPR is selected for transmission from several alternative OFDM signals which are obtained by applying inverse fast Fourier transform (IFFT) to each alternative symbol sequence that is an input symbol sequence multiplied by one of the phase sequences. In the PTS scheme, the input symbol sequence is partitioned into a number of disjointed subsequences. IFFT is applied to respective subsequences and the signals of subsequences are summed after they are multiplied by a set of rotating factors.
In SLM and PTS, the side information must be transmitted to enable the receiver to search the original OFDM symbol sequence. Such side information causes slight degradation in bandwidth efficiency. Moreover, incorrect detection of side information at to the receiver results in critical degradation of bit error rate (BER). For this reason, the side information must be highly protected so as not to affect the error performance of OFDM systems. Several blind SLM (BSLM) and blind PTS (BPTS) schemes to eliminate the need for side information have been studied. Maximum Likelihood (ML) decoders, which exhibit good BER performance, are derived for the BSLM and BPTS schemes. However, the conventional BSLM and BPTS schemes result in large decoding complexity at the receiver.
In the OFDM systems, an input symbol sequence X=[X0, X1, . . . , XN-1] is given as a vector of complex-valued symbols with the time duration Ts. After splitting the serial data into parallel data streams, all substreams are summed by applying IFFT.
The discrete time OFDM signal after IFFT is given as Expression 1:
            x      k        =                  1                  N                    ⁢                        ∑                      n            =            0                                N            -            1                          ⁢                              X            n                    ⁢                      ⅇ                          j2π              ⁢                              n                N                            ⁢              k                                            ,          ⁢      0    ≤    k    ≤          N      -      1      
where Xn is the input data symbol loaded on the n-th subcarrier and N is the number of the subcarriers. X is a vector of N constellation symbols from a given constellation Q. The size of Q is q.
Let x=[x0, x1, . . . , xN-1] be an OFDM signal sequence. The PAPR of x is defined by Expression 2:
      PAPR    ⁡          (      x      )        ⁢      =    Δ    ⁢                    max                  0          ≤          k          ≤                      N            -            1                              ⁢                                              x            k                                    2                    E      ⁢              {                                                        x              k                                            2                }            
where E{·} denotes the expectation. When all of 1 sequences are an input to N-point IFFT, the output signal is an impulse sequence with amplitude  at k=0. Thus, the theoretical maximum of the PAPR for N number of subcarriers is 10 log(N) dB.
Below, the conventional BSLM will be described.
For an input symbol sequence X, SLM generates U independent alternative symbol sequences and transmits the OFDM signal sequence with the minimum PAPR. U alternative symbol sequences are generated by multiplying X by U phase sequences. Suppose that U phase sequences are given as Expression 3:Pu=[ejφ0u, ejφ1u, . . . , ejφN-1u]where φnuε[0, 2π) and uε{1, 2, . . . U}. Let a{circle around (×)}b represent the componentwise multiplication of vectors a and b. For an input symbol sequence X, xũ=IFFT(X{circle around (×)}Pũ) with the minimum PAPR among U alternative signal sequences xu=IFFT(X{circle around (×)}Pu), 1≦u≦U is selected for transmission. The index ũ of the selected phase sequence should be transmitted to the receiver in the SLM scheme.
In order to eliminate transmission of the side information, a BSLM scheme wherein the indices are embedded into alternative signal sequences without loss of data rate was proposed in the related art. BSLM enables the receiver to distinguish the selected phase sequence from others without transmitting any side information.
It is assumed that the receiver receives r=xũ+n, where r=┌r1, r2, . . . , rN-1┐=FFT(R) and R is a received symbol sequence. To derive the input symbol sequence without the side information ũ from r at the receiver, U phase sequences in the BSLM scheme should have the following properties:
1. The set of Pus is fixed and known a priori; and
2. X{circle around (×)}Pu and X{circle around (×)}Pu are sufficiently different for u≠v.
To decode the input symbol sequence at the receiver, each phase φnu for all n and u must satisfy the condition of Xnejφnu∉Q. The set of Pu should be duly chosen to ensure this condition. If u≠ũ and channel noise is not considered in decoding OFDM symbols, each element of R{circle around (×)}Pu* will not be a symbol in the constellation Q where Pu* is the conjugate of Pu. Therefore, by using this result, a simplified ML decoder for the BSLM scheme can be derived to recover the OFDM symbol without the side information. Specially, when the Euclidian distance between any Pu and Pv is very large, BER performance of the ML decoder is expected to be very good.
The received symbol Rn after the FFT demodulation at the receiver may be written as Expression 4:Rn=GnXnejφnũ+{circumflex over (N)}n 
where Gn is the frequency response of the fading channel at the n-th subcarrier and {circumflex over (N)}n is an additive white complex Gaussian noise (AWGN) sample at the nth subcarrier.
Without the side information of ũ, the optimal ML decoder computes the decision metric for decoding the received symbol sequence R. The optimal metric of the ML decoder is given as Expression 5:
      D    opt    =            min                                    [                                                            X                  ^                                0                            ,                                                X                  ^                                1                            ,              …              ⁢                                                          ,                                                X                  ^                                                  N                  -                  1                                                      ]                    ⊆                      Q            N                                                P            u                    ,                      u            ∈                          {                              1                ,                2                ,                …                ⁢                                                                  ,                U                            }                                            ⁢                  ∑                  n          =          0                          N          -          1                    ⁢                                                                            R                n                            ⁢                              ⅇ                                  -                                      jϕ                    n                    u                                                                        -                                          G                n                            ⁢                                                X                  ^                                n                                                              2            
where |·| denote the absolute value of a complex number. This algorithm has to search all qN symbols for q-ary constellations that are repeated for each of P1, P2, . . . , PU.
Consequently, the overall decoding complexity to compute Expression 5 is UqN|·|2 operations.
Since decoding complexity from real additions is negligible as compared to that of |·|2 operations, the additions will be ignored. Since the decoder exhaustively searches all input symbol sequences, it can be performed only for small N. Thus, a suboptimal decoding method with reduced complexity should be derived.
Assume that n is detected into the nearest constellation point {circumflex over (X)}n. That is, a soft decision value is made for each subcarrier unlike the optimal ML decoder and the nearest constellation point from n is saved for each subcarrier. This process is repeated for 1≦u≦U. Therefore, the suboptimal decision metric of the ML decoder may be written as Expression 6:
      D    so    =            min                        P          u                ,                  u          ∈                      {                          1              ,              2              ,              …              ⁢                                                          ,              U                        }                                ⁢                  ∑                  n          =          0                          N          -          1                    ⁢                        min                                                    X                ^                            n                        ∈            Q                          ⁢                                                                                          R                  n                                ⁢                                  ⅇ                                      -                                          jϕ                      n                      u                                                                                  -                                                G                  n                                ⁢                                                      X                    ^                                    n                                                                          2                    
The input symbol sequence is recovered from the decoded symbol sequence having Dso. Though the complexity of suboptimal decoder is reduced to UqN|·| operations, it is still not practical.